· Lecture
notes (preliminary
version)
· Good to
know: (i) Some topics in Commutative Algebra (used in the Algebraic
Geometry course) will be
treated in more depth in the course Commutative
Algebra 2018/19 taught by Prof. R. Schoof
(ii)
There will be some intersection (with a different perspective) with the course Representation
Theory 1 2018/19 taught by Prof.ssa M. Lanini
· M. Atiyah
, I. G. Macdonald :
Introduction
To Commutative Algebra, Addison-Wesley Series in Mathematics(IN BIBLIOTECA)
· F. Bottaccin: Introduzione alla Geometria Algebrica, 2010/11
· C. Ciliberto
: Drafts of “Algebraic Geometry” course
· O. Debarre: Introduction à la géométrie algébrique,e, cours de DEA, 1999/2000, et M2, 2007/2008.
· I. Dolgachev
: Introduction to algebraic
geometry, 2013
· W. E. Fulton
: Algebraic
Curves. An introduction to algebraic geometry, 2008
· A.
Gathmann: Algebraic
Geometry, Notes for a class taught at the University of Kaiserslautern,
2002/03
· J. Harris : Algebraic
geometry (a first course), Graduate Texts in Math. No. 133. Springer, New
York-Heidelberg, 1977 (IN BIBLIOTECA)
· R. Hartshorne : Algebraic
Geometry, New York: Springer-Verlag, 1977. (IN
BIBLIOTECA)
· B. Hassett:
Introduction
to algebraic geometry, Cambridge University Press. 2007 (IN BIBLIOTECA)
· K. Hulek:
Elementary
Algebraic Geometry, Student mathematical library, vol. 20. 2003 AMS
·
K.
Kendig: "Elementary
Algebraic Geometry", Dover Books on Mathematics, second edition, Dover
Publications, 2015.
·
J.
MIlne : Algebraic Geometry,
Notes on-line
·
D. Mumford : "The
Red Book of Varieties and Schemes", LNM 1358, Springer (IN BIBLIOTECA)
·
M. Reid : Undergraduate
Algebraic Geometry, London Math. Soc. Student Texts, vol. 12, 1988,
Cambridge University Press
·
I. Shafarevich
: Basic
Algebraic Geometry, I. Springer-Verlag, New York-Heidelberg, 1977. (IN BIBLIOTECA)
· E. Sernesi
: Private Notes "Algebraic Geometry Course".
· E. Sernesi : "Appunti sui divisori speciali", typewritten handouts.
·
E. Sernesi
: "Una breve introduzione alle curve algebriche", Nervi
1984: Scanned pdf and translation in english (by C.Fontanari)
· K. Ueno: An Introduction to Algebraic Geometry 1997.(IN BIBLIOTECA)
· A. Verra : Introduzione alle curve algebriche piane, Alfaclass Summer School
·
G. Fano
· C. Segre
·
A. Weil
Exams/Learning aims
* Exam Oral examination
* Learning aims Our general scope is to present
fundamental concepts related to the problem of solvings
systems of polynomial equations. Algebraic Geometry studies these solutions
from a “global” point of view, through the theory of Algebraic Varieties.
We will define this important class of varieties and then we will study some of
their most important properties and discuss key examples, which are fundamental
for the whole theory. Learning aims are to give to students the following
skills:
·
working knowledge of basic elements of affine/projective geometry, of homomorphisms, isomorphisms and
rational maps among algebraic varieties;
·
familiarity with explicit examples, including plane curves, quadric
surfaces, Grassmannian of lines, Veronese and Segre
varieties, etc;
·
if time permits, familiarity with the rich geometry of the canonical
curve in terms of special linear series.